write me an example problem for finding inverse functions. dont tell me the answer till i say so

Here’s an example problem for finding inverse functions:

### Problem:
The function \( f(x) = \frac{3x - 2}{x + 1} \) is defined for all \( x \neq -1 \).

1. Find the inverse function, \( f^{-1}(x) \), if it exists.
2. State the domain and range of both \( f(x) \) and \( f^{-1}(x) \).

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Let me know when you're ready for the solution or if you have any questions! 

Here are **5 related questions** to expand your understanding:
1. What conditions must be met for a function to have an inverse?
2. How do you verify that two functions are inverses of each other?
3. What happens if a function is not one-to-one? Can it still have an inverse?
4. How do domain restrictions affect the existence of an inverse function?
5. Can you find the inverse of \( f(x) = x^2 \) if the domain is \( x \geq 0 \)? 

### Tip:
When solving for the inverse, swap \( x \) and \( y \) (where \( y = f(x) \)) and solve for \( y \) to find \( f^{-1}(x) \).

Learn how to find the inverse of the function f(x) = (3x - 2) / (x + 1) with a detailed step-by-step guide. This problem covers key concepts such as inverse functions, domain and range, and the conditions for a function to have an inverse. Suitable for students in Grades 10-12.

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